COHERENT OPTICAL TRANSCEIVER BASED ON CO-PRIME SAMPLING
3.1 Introduction
Integrated optical beamforming and image processing has many applications rang- ing from point-to-point optical communications, 3D imaging, LIDAR for airborne imaging and autonomous vehicles, compact, lens-free projection systems, lens-free imagers, holographic recording, and projection. In conventional optical systems, image processing and reconstruction is achieved using discrete optical elements such as lenses, mirrors, and beamsplitters, and beamforming and scanning is done using mechanical stages. This adds to the cost as well as the complexity of the system. On the other hand, integrated photonic platforms allow for high-density integration of photonic components resulting in a smaller size and increased sys- tem complexity. The theoretical potential of optical beamforming was inspired by its RF and microwave counterparts [46]β[48] and early demonstrations of optical beamforming date back to the early 1960s-70s [1,2]. In fact, several integrated photonic beamforming systems have been demonstrated [5]β[7]. On the other hand, the emergence of CMOS-compatible silicon integrated photonics has allowed for the realization of integrated photonic beamforming at lower costs with improved yield using silicon-based dielectric waveguides and radiators [10], [12], [45]. Vari-
1This work was done in collaboration with Reza Fatemi.
ous sub-systems for improving the performance of integrated optical beamformers such as high-efficiency integrated modulators [43], [49], high-efficiency radiating elements [50], [51], and integrated on-chip calibration [52] have been proposed.
The trend in SiP OPA integration for greater than one hundred radiating element is to place radiating elements on a one-dimensional grid and beamforming in one di- mension using integrated phase-shifters. Beamsteering in the orthogonal direction is achieved using long and wavelength sensitive grating couplers [50] by sweeping the wavelength of the laser. Very large arrays of 512 to 8192 radiating elements in a one-dimensional array have been demonstrated in the past [43], [53], [54]. This architecture is referred hereon as 1D-OPA, while architectures that have radiating elements placed on a 2D grid are referred to hereon as2D-OPA. 1D-OPA architec- tures have several shortcomings. This architecture requires a widely tunable and low linewidth laser, which adds to the cost and system complexity. The wavelength tun- ability requirements for this type of phased array is 100nm or more [55]β[58]. At the extreme case, a class of phased arrays requires only a tunable source for beamsteer- ing called serpentine arrays [59], [60]. This architecture also requires over 100nm of wavelength tunability for beamsteering. Radiation beam-angle is very sensitive to the wavelength of the laser, and henceforth precise control of the laser wavelength and linewidth is required to control the beam direction. In addition, multi-beam operation using complex beamforming techniques and multi-wavelength operation without increasing the number of required sources is not possible with this method.
This design choice primarily rises from the dielectric nature of the optical waveg- uides as well as radiating elements in SiP OPAs. In this platform, the dimension of the waveguides and radiating elements are in the order of the wavelength and require sufficient spacing between these SiP devices to prevent undesired coupling between individual signal lines via waveguide and between radiating elements. In a planar photonic platform, a 2D-OPA requires a minimum spacing between radiating ele- ments to allow for the signal to be routed to the radiators in the center of the radiator array (Fig. 3.1). On the other hand, creating large-scale integrated beamformers with a large field-of-view requires placing the elements at half-wavelength spac- ing. The fabrication limitation of planar OPA and the dielectric nature of placing the element at larger spacing reduced the usable field-of-view of the phased array.
Previously demonstrated silicon photonic 2D-OPAs have a very limited FOV [10], [11], [45].
The trade-off between FOV and number of radiating elements for a typical scenario
Figure 3.1: Routing optical signal to radiating elements in a 2D grid requires a larger inter-element spacing. 5π/2 element spacing results in less than 30β¦FOV.
of 2ππΓ 2ππ grating couplers, with 500ππ-wide waveguides and 1ππ spacing between elements, is plotted in Fig. 3.2. If all waveguides are routed from a single side to the apertures for a 10Γ10 OPA, the field-of-view will have an upper bound of 2.3β¦. Even for an optimized routing where waveguides are routed through all 4 sides of the aperture, the FOV will have an upper bound of 6.2β¦. Furthermore, it can be seen that FOV gain for multi-layer routing diminishes for a given number of radiating elements. In the case of a two-layer photonics process with twice as many antenna feed paths, the upper bound of the FOV is 8.7β¦. Henceforth, uniform array beamforming architectures FOVs will be limited to less than 10β¦ for a sufficiently large number of elements.
Several methods are developed to address this issue in 2D-OPAs. For example, the radiating element can be placed next to the phase and amplitude modulators for that radiator as a unit cell several wavelengths in diameter [10], [45]. This method trades the usable field-of-view of the integrated beamformer with the capacity for large-scale integration. Prior arts using this architecture have a limited FOV of a few degrees. Another challenge with these unit-cell-based OPAs is the power consumption of the phase shifter and amplitude modulator. Only thermo-optic (TO) modulators are sufficiently small enough to be integrated into the unit-cell, and static power consumption is required to maintain the desired phase and amplitude. Thus,
Figure 3.2: OPA FOV as a function of the number of elements in the array. A signal distribution waveguide pitch of 1ππ and radiating element size of 2ππ Γ2ππ is assumed. The FOV is severely limited once the total number of elements in the array is above 50.
the power consumption of this architecture will scale with the aperture size, and heat management will become an issue. Another method to address the FOV and radiating element count trade-off is using sparse (thinned) arrays. This type of array has been previously constructed in RF and microwave domains for the purpose of reducing the number of required radiating elements and phase modulators. Thinned arrays, minimum redundancy arrays, vernier arrays, MIMO arrays, and nested arrays [46], [61]β[64] are a few examples of sparse architectures in RF, and some of these have been proposed and/or demonstrated for optical integrated phased arrays [17], [65]β[67]. The non-uniform element placement of the radiating elements in this array architecture achieves a narrow beamwidth without reducing the field-of-view with a fewer number of elements compared to the same number of uniformly spaced radiators. The trade-off in this architecture is between the number of radiating ele-
ments and the radiation efficiency (total power in the main beam) which is known as the array sparsity curse. Here, the projected power of the main beam is reduced and spreads in undesired directions. It is only the case in uniform sampling that the power of the main beam goes to equally spaced grating lobes, and the power in the side-lobes (scattered in undesired directions) is minimized. In RF and microwave beamforming, several architectures have been proposed to create a sparse array with deterministic spacing between radiating elements such as minimum redundancy ar- rays, MIMO arrays, nested arrays, vernier arrays, etc, all of which can be applied to SiP OPAs. The design choice for an optical beamforming method should op- timize the required number of radiating elements, achieve superior beamforming performance, and address the planar routing constraints of the SiP platform. More importantly, laser sources are the dominant source of power consumption in SiP in- tegrated systems, and optical amplifiers are inefficient compared to their electronics counterparts. As a result, power management is very critical. Therefore, beam- forming methods that have efficient beamforming with uniformly spaced elements and apodized amplitude that utilizes analog array gain are preferred. Also, complex optical modulators with high insertion loss are less desirable.
Transceiver arrays utilizing co-prime beamforming techniques are one method that satisfies all these requirements. Co-prime beamforming is achieved by placing transmitter array elements in a uniform grid with an inter-element spacingππ π and receiver element with uniform inter-element spacing ofππ π, whereππ π andππ πare co-prime with respect to each other. These uniform arrays only require basic phase and amplitude control and offer array gain before amplification and hence have SNR advantage. Half-wavelength spacing is not required between radiating elements, and henceforth, 2D routing constraints are relaxed. Furthermore, mutual coupling between the radiating elements is reduced [68]. Finally, the co-prime sampling technique offers an optimum number of radiating elements for a given transmitter and receiver inter-element spacing. It is shown that withπ(π) beamforming elements, it is possible to achieveπ(π2) resolvable points (PPV). This system allows multi- beam operation for imaging by incorporating multiple receivers or a multi-beam receiver. This system achieves a quadratically larger resolvable spot compared to its radiators without sacrificing SNR and field-of-view. The background formulation of co-prime sampling is explained in Section II, the design of two co-prime OPAs are described in Section III, measurement in IV, and discussion in V.